%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO183+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:17:19 AM UTC 2026
% Result : Theorem 0.16s 5.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 13 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('theBenchmark.p',a4) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(Y,U)
& incident_point_and_line(X,U) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(Y,U)
& incident_point_and_line(X,U) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( ~ distinct_lines(A,B)
| ~ equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(Y,U)
| ~ incident_point_and_line(X,U) )
& equal_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ incident_point_and_line(sK2,sK0)
| ~ incident_point_and_line(sK1,sK0) )
& equal_lines(sK0,line_connecting(sK1,sK2))
& convergent_lines(sK0,sK3)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0,sK3]),skolemize(X,sK1),skolemize(Y,sK2),skolemize(U,sK0),skolemize(V,sK3)],[nnf_36]) ).
cnf(c_41,negated_conjecture,
equal_lines(sK0,line_connecting(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_46,negated_conjecture,
~ distinct_lines(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_41]) ).
cnf(c_53,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_54,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_59,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_81,plain,
( apart_point_and_line(A,B)
| incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
cnf(c_82,negated_conjecture,
distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_84,negated_conjecture,
( ~ incident_point_and_line(sK2,sK0)
| ~ incident_point_and_line(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_94,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_82,c_54]) ).
cnf(c_95,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_82,c_53]) ).
cnf(c_103,plain,
( apart_point_and_line(sK2,sK0)
| ~ incident_point_and_line(sK1,sK0) ),
inference(resolve,[status(thm)],[c_84,c_81]) ).
cnf(c_163,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_59,c_46]) ).
cnf(c_118,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_163,c_94]) ).
cnf(c_119,plain,
~ incident_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_118,c_103]) ).
cnf(c_121,plain,
apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_119,c_81]) ).
cnf(c_164,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_59,c_46]) ).
cnf(c_165,negated_conjecture,
~ apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_164,c_95]) ).
cnf(c_162,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_121,c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO183+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n020.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Fri Sep 25 13:03:40 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.40 % Process 2979915 was started by sandbox on n020,
% 0.12/5.40 % Fri Sep 25 13:03:40 2026
% 0.12/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.41
% 0.16/5.41 % From the command line: assign(max_seconds, 300).
% 0.16/5.43
% 0.16/5.43 % SZS status Theorem for theBenchmark
% 0.16/5.43
% 0.16/5.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/5.43 % Length of proof is 22.
% 0.16/5.43 % Level of proof is 6.
% 0.16/5.43 % Maximum clause weight is 18.000.
% 0.16/5.43 % Given clauses 55.
% 0.16/5.43
% 0.16/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------